We investigate the design of observers for non-integrable nonlinear single-output systems, i.e., systems that cannot be transformed into observer canonical form. Inspired by flat input based methods, we use dynamic compensation to alter the original dynamics such that the modified system can be transformed into observer canonical form. We construct a canonical form observer for the modified system. Utilizing the compensators, we can then deduce the state of the original dynamics. The method is demonstrated on well-known non-integrable examples.